You can excite with an AC voltage source and measure the current or use a current source and measure the voltage.
then you know that:
V/I = Z = R/ (1+ jwRC) that is the impedance of the RC circuit.
w = 2* pi * frequency
Take into account that V, I and Z are complex numbers. So you have to measure magnitude and phase.
Calculate V/I from your measurements. You also know at what frequency the measurement took place.
Rearrange the expression of Z and convert V/I so both have the form a+jb.
Re(V/I)= Re(Z) -- gives R
Im(V/I)=Im(Z) -- knowing w allows you to calculate C.
Hope that this is not very confusing